Murchison wills at familysearch.org=free site, requires registration but no fees.You need to access the US collection, then North Carolina records, then North Carolina probate records, then to Moore Co., NC. Once in Moore Co., NC selections, I indexed Murchison by index for wills, and Kennith/Kenneth Murchison left a will in Will Book B, page 88-91 which indeed named a son Murdock Murchison and will says Kennith Senr. The images for the will will be a series of 166 but the will itself will be images beginning with 68/166.If you have trouble transcribing etc. let me know. All the names of the children of Kennith/Kenneth Murchison show these children were by mother's named Catherine!(1st wife, apparently deceased, and second wife Catherine, living). This will was dated 18 June 1834 and numerous children of this man existed.
The records of appt. of administrations of estates shows that in 1789 Kennith was appt. admr. of estate of Alexander McGlaughlin which considering a son, Alexander Murchison, could suggest (and I mean suggest) his wife Catherine could have been a McGlaughlin. (No relationship to my married surname).